For the universal set U, if n(U)=72 and n(A^c)=3n(A), what is the value of n(A)?
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Answer and explanation
Correct answer: 18
Let n(A)=x. For a finite universal set, A and its complement A^c are disjoint and together contain every element of U. Therefore, n(A)+n(A^c)=n(U). Substituting n(A^c)=3n(A), n(U)=72, and n(A)=x gives x+3x=72, so 4x=72 and x=18. Thus, option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Let n(A)=x. For a finite universal set, A and its complement A^c are disjoint and together contain every element of U. Therefore, n(A)+n(A^c)=n(U). Substituting n(A^c)=3n(A), n(U)=72, and n(A)=x gives x+3x=72, so 4x=72 and x=18. Thus, option A is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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